Download Mammal Reproductive Strategies Driven by Offspring Mortality

vol. 173, no. 6
the american naturalist
june 2009
E-Article
Mammal Reproductive Strategies Driven by Offspring
Mortality-Size Relationships
Richard M. Sibly1,* and James H. Brown2
1. School of Biological Sciences, University of Reading, Reading RG6 6AS, United Kingdom; and Centre for Integrated Population
Ecology, Department of Environmental, Social and Spatial Change, Roskilde University, DK-4000 Roskilde, Denmark; 2. Department of
Biology, University of New Mexico, Albuquerque, New Mexico 87131; and Santa Fe Institute, Santa Fe, New Mexico 87501
Submitted July 15, 2008; Accepted November 11, 2008; Electronically published April 17, 2009
abstract: Trade-offs have long been a major theme in life-history
theory, but they have been hard to document. We introduce a new
method that reveals patterns of divergent trade-offs after adjusting
for the pervasive variation in rate of resource allocation to offspring
as a function of body size and lifestyle. Results suggest that preweaning vulnerability to predation has been the major factor determining how female placental mammals allocate production between
a few large and many small offspring within a litter and between a
few large litters and many small ones within a reproductive season.
Artiodactyls, perissodactyls, cetaceans, and pinnipeds, which give
birth in the open on land or in the sea, produce a few large offspring,
at infrequent intervals, because this increases their chances of escaping predation. Insectivores, fissiped carnivores, lagomorphs, and
rodents, whose offspring are protected in burrows or nests, produce
large litters of small newborns. Primates, bats, sloths, and anteaters,
which carry their young from birth until weaning, produce litters of
one or a few offspring because of the need to transport and care for
them.
Keywords: life-history theory, trade-off, litter size, offspring size, litter
frequency, litter mass.
Introduction
A synthetic conceptual framework that can account for
the wide variation in mammal life histories has remained
elusive, despite decades of vigorous theoretical investigation (e.g., Charnov 1991, 2001; Kozlowski and Weiner
1997; Oli 2004; Dobson 2007), meticulous collection and
analysis of data (e.g., Gaillard et al. 1989; Promislow and
Harvey 1990; Purvis and Harvey 1995; Jones and MacLarnon 2001; Charnov and Ernest 2006; Bielby et al. 2007),
and a rich literature documenting how females allocate
resources to reproduction (Charnov et al. 2007). It has
long been recognized that the mass-specific rate of biomass
production scales allometrically with adult female body
* Corresponding author; e-mail: [email protected].
Am. Nat. 2009. Vol. 173, pp. E185–E199. 䉷 2009 by The University of
Chicago. 0003-0147/2009/17306-50605$15.00. All rights reserved.
DOI: 10.1086/598680
mass, M, as approximately M⫺1/4 to M⫺1/3. This is similar
to the scaling of mass-specific metabolic rate, which fuels
the growth and development of offspring through gestation and lactation (Brown et al. 2004). Recently, we have
shown that productivity differs between taxonomic and
lifestyle groups of mammals in predictable ways (Sibly and
Brown 2007). A lifestyle is a way of making a living that
is made possible by a unique combination of anatomical,
physiological, and behavioral traits. Productivity increases
when adaptations exploit abundant, reliable food supplies,
and it decreases when adaptations reduce predation. The
evolution of these combinations appears to be relatively
conservative, so lifestyles are typically deeply rooted in
clades and widely shared within taxonomic groups. Evidence of their adaptive significance comes from their independent and convergent evolution in distantly related
lineages. These lifestyle adaptations represent a second major axis of life-history variation, orthogonal to the pervasive effect of body mass (Brown and Sibly 2006; Dobson
2007; Sibly and Brown 2007). Here we consider how much,
how often, and why production is allocated to individual
offspring and evidenced in the fundamental life-history
trade-offs.
Traditionally, both theoretical and empirical analyses of
life histories have focused on hypothesized trade-offs: for
example, between survival and reproduction, between
“fast” and “slow” life histories, between juvenile and adult
survival, and between the numbers and sizes of offspring.
Many attempts to analyze these trade-offs have not explicitly considered the fundamental allometries of production and survival. For example, there is necessarily a
negative correlation between production and survival:
smaller animals with higher birth rates must have correspondingly higher death rates. Similarly, for animals of the
same size, adaptations that increase production necessarily
result in increased death rates (reduced survival) as a result
of “ecological compensation” (Sibly and Calow 1986, 1987;
Sutherland et al. 1986).
Several recent analyses of life histories have explicitly
E186 The American Naturalist
considered allometric correlates of body size (e.g., Gaillard
et al. 1989; Charnov 1993; Bielby et al. 2007; Dobson 2007;
Sibly and Brown 2007). These have called attention to
other hypothesized trade-offs such as that between number
and size of offspring or between juvenile and adult survival, which are not direct consequences of the allometry
of production but instead depend on how production is
allocated among different components of the life history.
Such trade-offs should be evidenced as negative relationships in the residual variation that remains after accounting for the allometry of production within and between
taxonomic and lifestyle groups. They can be empirically
evaluated most powerfully and realistically by manipulating the relevant variables, such as in field experiments that
manipulate clutch size and nest predation in birds (e.g.,
Fontaine and Martin 2006) or allocation to egg yolk in
reptiles (e.g., Sinervo and Huey 1990). Similar experiments
with eutherian mammals are more difficult because females retain developing embryos within the body during
gestation and nourish them during lactation. Nevertheless,
these unique features of mammalian life history offer opportunities to develop and test a more general and comprehensive theoretical framework.
Here we consider two potential trade-offs in how production is allocated to reproduction: (1) between the number of offspring in a litter and the size of the offspring
and (2) between the number of litters and the biomass of
each litter produced over a reproductive season. Our approach differs from that of most recent analyses in that it
is explicitly mechanistic. We focus on variation among
species, taxa, and lifestyle groups in the rate of massspecific production and how this energy is allocated within
and among litters.
Theoretical Framework and Predictions
Conservation of mass and energy constrains how resources
are divided among multiple functions, so allocating more
to one function means that less is available for allocation
elsewhere. This “principle of allocation” has long been a
fundamental assumption of life-history theory (Cody
1966). We use the principle twice here. First, productivity,
measured as reproductive biomass produced per year, is
assumed to be the product of litter mass and litter frequency, as in equation (3a). Second, litter mass is the
product of offspring size and number, as in equation (3b).
Resources are assumed to be allocated so as to maximize
the Darwinian fitness of the life history, which we define
as the per-copy rate of increase of a gene for a specified
set of life-history traits (Charlesworth 1980; Sibly and Curnow 1993). Darwinian fitness is given by an analog of the
Euler-Lotka equation. The simplest life history that embraces the complexity we need has two stages—juvenile
and adult—and for each we require measures of survivorship and duration. We distinguish the stages by subscripts (j for juvenile and a for adult) and let S and t
denote survivorship and durations, respectively. Thus Sj
and Sa represent juvenile and adult survivorship, tj is the
age at first breeding, and ta is the interval between breeding
attempts, each of which results in n offspring. Then the
Euler-Lotka equation defining fitness, F, is
1
1 p nS j e⫺Ft j ⫹ Sae⫺Ft a
2
(1)
(Sibly and Calow 1986). The central aim of life-history
theory is to find the life-history parameters n, tj, ta, Sj, and
Sa that maximize F subject to constraints imposed by the
principle of allocation, that is, equations (3a) and (3b).
Our immediate objective here is to find optimal offspring
mass, but this depends on its effects on life-history variables. The simplest possibility is that offspring size affects
only n, being inversely proportional as a result of the principle of allocation. Alternatively, it may also affect juvenile
survivorship and/or age at first reproduction, the first being more important here; this is illustrated in figure 1B.
In figure 1A and 1C, offspring size has no effect on juvenile
survivorship, and the optimal strategy is to produce offspring as many and as small as possible. In figure 1B and
1D, offspring size has a marked positive effect on juvenile
survivorship, but there are diminishing returns, so the
optimal strategy is to produce offspring of intermediate
size. Thus, everything else being equal, natural selection
favors higher birth rates and hence many small offspring
(fig. 1A, 1C). Everything else is not always equal, however,
and larger offspring can be adaptive if juvenile survivorship increases with offspring size (fig. 1B, 1D). Additionally, everything else being equal, natural selection favors
producing many small litters rather than a few large ones
so as to avoid the chance that the mother dies or the litter
is discovered by a predator before it can be weaned. Again,
however, circumstances of lifestyle and ecology, such as
restrictive seasonal breeding opportunities, can override
this tendency.
In testing predictions we “corrected for” the variation
in production with body mass and across different taxonomic and lifestyle groups by fitting parallel-line models,
as in figure 2. Each line (color coded in fig. 2) corresponds
to a different functional or taxonomic group. This procedure is justified theoretically and empirically for the data
of figure 2A in Sibly and Brown (2007), which shows how
variation in production rate orthogonal to the body size
axis is due to lifestyle. Because both body size and lifestyle
affect production, both may affect its components, so these
also were analyzed using parallel-line models as detailed
below. Parallel-line models are appropriate because our
Mammal Reproductive Strategies E187
Figure 1: How neonate size may affect juvenile survivorship (A, B) and Darwinian fitness (C, D). Graphs plotted using equation (1) with parameter
values n # neonate size p 10, tj p ta p 1, Sa p 0.9.
main interest is in comparing the heights of the lines (as
quantified by the intercepts, i.e., normalization constants
of the allometric equations). Following Sibly and Brown
(2007) for a life-history trait w, we regressed log w on
log M to obtain a regression equation of form
log w p wi ⫺ bw log M,
(2)
where wi is a normalization constant (equivalent to a yintercept) specific to the ith taxonomic or lifestyle group,
bw is the regression coefficient of trait w and is assumed
to remain constant across all groups, and M is adult female
body mass. Let x denote (neonate mass)/(adult body
mass), n be offspring per litter, z be (litter mass)/(adult
body mass), y be the number of litters produced each year,
and q be mass-specific production. Because (litter mass)/
(adult body mass), z, is defined as the product x # n, and
because mass-specific production, q, is defined as the product z # y, we have
log q p log z ⫹ log y,
(3a)
log z p log x ⫹ log n,
(3b)
and combining these equations with equations of the form
of equation (2), we have, using obvious notation,
q i ⫺ bq log M p z i ⫺ bz log M ⫹ yi ⫺ by log M,
(4a)
z i ⫺ bz log M p x i ⫺ bx log M ⫹ ni ⫺ bn log M.
(4b)
Equating coefficients, we have
bq p bz ⫹ by ,
(5a)
bz p bx ⫹ bn ,
(5b)
q i p z i ⫹ yi ,
(6a)
z i p x i ⫹ ni .
(6b)
and
Thus, our modeling approach is predicated on the assumption that each of the life-history traits should scale
allometrically with body mass, as in equation (2). Our
method of obtaining the normalization constants of specified taxonomic or lifestyle groups is shown in figure 3A.
To analyze for trade-offs between pairs of traits that are
due to the principle of allocation, the normalization constants for the two traits are plotted against each other, as
shown in figure 3B. In the simple case illustrated in figure
3B, there is no variation between the three lifestyle groups
in the quantity of resource, z, being allocated. In more
complicated cases, it is necessary to allow for variation
between lifestyle groups in their z normalization constants,
and for this reason strategies with the same values of z are
indicated by dashed brown lines in figures 4 and 5. Where
desired, allowance for variation in z values can be achieved
by moving points perpendicular to the z contours and
assembling them on a common reference contour, as
E188 The American Naturalist
shown in figure 3C. The relative positions of the standardized points are the same irrespective of which z contour is chosen for standardization. This procedure allows
analysis of trade-offs after standardization for the quantity
of resource available for allocation.
This conceptual framework allows us to predict theoretically and evaluate empirically how natural selection,
responding primarily to the sensitivity of juvenile survivorship to neonate size, as in figure 1, has shaped the life
histories of eutherian mammals. We now use this framework to make bold statements about the allocation strategies of different taxonomic and lifestyle groups and about
the environmental conditions that have shaped the tradeoffs. These statements represent plausible testable hypotheses that are consistent with current information on mammal life histories. Our hypotheses/predictions are:
1. A trade-off between number and size of offspring in
a litter will be evidenced as a negative correlation among
the normalization constants of the lifestyle groups. Groups
that produce larger offspring should have smaller litters.
2. Artiodactyls, perissodactyls, cetaceans, and pinnipeds
should give birth to a relatively small number of large,
precocial offspring. Their offspring are born unprotected
on the ground or in the sea. Offspring survival depends
critically on offspring size, as in figure 1B, because large,
well-developed offspring are better able to escape predators
and require less time to mature. Additionally, thermoregulation is enhanced by the larger size and better insulation
of the precocial condition.
3. Primates, bats, sloths, and anteaters should also have
a few large offspring. These mammals mostly carry their
young, which reduces risk of predation but limits the number because newborn offspring must be sufficiently developed to hold on and to thermoregulate outside the
protective microclimate of a nest or burrow. Additionally,
only a small number of offspring can be closely attended
while the mother forages, interacts with conspecifics, and
escapes from predators.
4. Insectivores, fissiped carnivores, lagomorphs, and rodents should produce large litters of relatively small altricial neonates. This should be true in particular for rep-
Figure 2: Variation in productivity (A) and the components of reproduction (B–E) as a function of body size. Productivity is measured as
specific production rate, y⫺1, defined as the product of (litter mass)/(adult
mass) and litter frequency (litters per year). (Litter mass)/(adult mass)
is the product of offspring per litter and (newborn mass)/(adult mass).
All scales are logarithmic to base 10. Symbols as in A throughout. The
lines in each panel have the same slopes and are color coded according
to taxon. The regression coefficients (slopes) are shown at the top right
of each panel. The four outlying data points for fissipeds to the right of
A, C, and E are bears of the family Ursidae. For clarity, only taxonomic/
lifestyle groups with ≥10 species are shown.
Mammal Reproductive Strategies E189
Figure 3: Schematic illustration of our analytical methods. A, First, the allometry of each trait is analyzed in a log-log plot (as in fig. 2). Here we
show three hypothetical traits, x, n, and z, in relation to body mass, indicated by dashed, solid, and dotted lines, respectively, for each of three
different lifestyle groups, a, b, and c, colored red, green, and blue. The variable z represents (litter mass)/(adult mass), n represents offspring per
litter, and x represents (offspring mass)/(adult mass), so for each lifestyle and for each adult mass, z p n # x and log z p log n ⫹ log x (see “Methods”).
At any body mass, a, b, and c all have the same value of trait z, but a has a higher value than b or c for trait n and a lower value for trait x. The
key characteristic of each lifestyle group is the relative height of its trait lines, which are indexed by their y-intercepts, here called normalization
constants. B, To analyze for trade-offs between traits, the normalization constants are plotted against each other, and a trade-off between traits x
and n is revealed by the negative slope. In this example, all three lifestyle groups have the same normalization constants for trait z, so their
normalization constants for traits n and x lie on a straight line, shown in brown, and the labeled points satisfy the equation log z p log n ⫹ log x.
In this case, the amount of resource being allocated, z, does not differ between the lifestyle groups when allometry of body mass is accounted for.
C, Generally the quantity of resource being allocated differs between lifestyle groups, so the points lie on different lines. We correct for this variation
by projecting trait values onto a standard reference line, as shown here.
resentatives of these groups that rear their dependent
young in burrows or nests, so that survival from birth to
weaning is not greatly affected by offspring size (see fig.
1A).
5. Putting together predictions 2–4, most mammals
should separate into two classes: those producing either a
few large, precocial offspring (artiodactyls, perissodactyls,
cetaceans, pinnipeds, primates, bats, and xenarthrans) or
many small, altricial offspring (insectivores, fissipeds, lagomorphs, and rodents).
6. The negative correlations predicted in hypothesis 1
should also be observed in the residuals for species within
lifestyle groups after accounting for the effects of body
size. So, for example, caviomorphs (guinea pigs and relatives) within the rodents, and hares within the lagomorphs, which give birth to precocial neonates, should
produce litters of fewer, larger offspring. The sea otter,
which differs from other fissiped carnivores in that it gives
birth at sea, where risk of predation and costs of thermoregulation are high, should also produce litters of a few
large, precocial neonates.
7. A trade-off between allocation per litter and number
of litters per reproductive season should be evidenced as
a negative correlation among the normalization constants
of the various taxonomic/lifestyle groups. Groups that produce more litters per year should allocate less production
to each litter.
Methods
We used recent compilations of mammalian life-history
data for placental, nonvolant mammals (Ernest 2003) and
for Chiroptera (K. E. Jones, unpublished data). These data
sets record offspring per litter, litters per year, neonate and
weaning masses, and adult body mass. Analyses were conducted for 628 species, representing 366 genera, 88 families, and 11 orders, for which data on offspring per litter,
litters per year, neonate mass, and adult body size were
available for at least five species per order. We did not
consider monotremes or marsupials, which are longdivergent lineages with dramatically different reproductive
biologies: egg laying and pouch rearing, respectively. The
availability of data dictates that we use the mass of offspring at birth to assess the predicted trade-off between
the size and number of offspring in a litter. We are aware
that female mammals typically allocate much more production to lactation than to gestation, but neonate mass
is a constant ratio of weanling mass within lifestyle groups
E190 The American Naturalist
Figure 4: Scatterplots analyzing the two trade-offs between number of litters per year and litter mass (A) and between number of offspring per
litter and offspring size (B) by plotting the normalization constants of the main mammal taxonomic/lifestyle groups. Numerical values of normalization
constants are given, together with their standard errors (which are generally !0.05) in table A1. Ellipses enclose the classes of mammalian life
histories referred to in the text. A, Litters per year as a function of (litter mass)/(adult mass). Dashed brown lines connect strategies having the
same values of specific production rate (q) and satisfy equation (6a). B, Offspring per litter as a function of (newborn mass)/(adult mass). Dashed
brown lines indicate strategies with the same values of (litter mass)/(adult mass) (z) and satisfy equation (6b) (see fig. 3 for a rationale). Logarithms
are to base 10.
and this ratio varies only from 0.10 to 0.30 among lifestyle
groups (Sibly and Brown 2007). Data manipulation and
statistical analyses were performed using Minitab 15.1, and
parallel lines of the form of equation (2) were fitted to
the data of figure 2 using general linear modeling.
Results
Mass-specific production rate and the other life-history
variables for 628 species of eutherian mammals are plotted
as a function of adult body mass on logarithmic axes in
figure 2. Figure 2A shows specific production rate, our
best estimate of annual resource investment in reproduction. Figure 2B and 2C shows how this is allocated among
the litters that are produced each year to determine litter
frequency (fig. 2B) and mass (fig. 2C). Figure 2D and 2E
shows how litter mass is divided among offspring according to their number. Notice that the parallel-lines model
generally fits the data well (fitting nonparallel-lines models
increases the adjusted R2 value by only 2%, 3%, 1%, 0%,
and 0% for fig. 2A–2E, respectively; tables A1, A3).
Values of the normalization constants and results of
ANOVAs are given for the parallel-lines model in table
A1, showing that the normalization constants differ mark-
edly among the taxonomic/lifestyle groups for each trait
(P K .001). Normalization constants for the different
groups based on taxonomy and lifestyle are plotted in
figure 4, and residuals for species within these groups are
plotted in figures 5 and A1.
These analyses can now be used to evaluate the predictions above.
1. A trade-off between the number and size of offspring
in a litter should be evidenced as a negative correlation
among the normalization constants for the taxonomic/
lifestyle groups. Figure 4B shows that these traits are indeed
negatively correlated (r9 p ⫺0.73, P p .01). To control
for lack of independence between closely related species,
we repeated these analyses using genus and family means
and found similar relationships (r9 p ⫺0.72 and ⫺0.79
for genus and family, respectively; P p .01; fig. A2).
2, 3. Two groups should have a relatively small number
of large precocial offspring: (i) artiodactyls, perissodactyls,
cetaceans, and pinnipeds, whose young are born unprotected in the open, and (ii) primates, bats, sloths, and
anteaters, which carry their young from birth until weaning. These predictions are supported. After standardization
for the rate of production using the method in figure 3,
there were differences between the precocial, the carried,
Figure 5: Scatter diagrams analyzing the two major trade-offs by plotting residuals within Artiodactyla (A, B), Lagomorpha (C, D), and Pinnipedia
(E, F). A, C, E, Litters per year as a function of (litter mass)/(adult mass). B, D, F, Offspring per litter as a function of (newborn mass)/(adult
mass). Residuals are calculated for each species from figure 2 as the vertical distance of the species from the lines of the same color in figure 2.
Thus, residuals represent the difference between log10 life-history traits and the values expected from the species’ body mass for members of the
species’ taxonomic/lifestyle group. Solid black lines are fitted regressions and are shown where correlations are significant (P ! .05 ; table 1). Dashed
brown lines connect strategies with the same resource allocation as in figure 4.
E191
E192 The American Naturalist
and the altricial groups (one-way ANOVA: F2, 8 p 71.4,
P ! .001). The precocial and the carried groups of figure
4B are farther to the right along a common z contour than
the altricial group (Dunnett’s multiple comparison tests:
P ! .001). Using genus and family means gave similar results (P ! .001; data in fig. A2), and the results are robust
to errors in the allometric regression coefficients (data in
fig. A3).
4. Insectivores, fissiped carnivores, lagomorphs, and rodents, whose offspring are protected in burrows or nests,
should have many small, altricial offspring. These groups
do indeed produce large litters of small offspring, as shown
in figure 4B (statistics as in evaluation of predictions [2]
and [3]). Outliers tend to be species such as caviomorph
rodents and hares, which give birth to well-developed
young in exposed environments (see [6], below).
5. Putting together predictions (2)–(4), most mammals
should separate into two classes, with litters containing
either a few large, precocial offspring (artiodactyls, perissodactyls, cetaceans, pinnipeds, primates, bats, and xenarthra) or many small, altricial offspring (fissipeds, insectivores, lagomorphs, and rodents). This is indeed the
observed pattern, as shown in figure 4B.
6. The negative correlations predicted in (1) should also
be observed among species residuals within lifestyle groups
after the effects of body size have been accounted for.
Scatterplots of residuals are shown in figures 5, A1, and
correlation coefficients are given in table 1. If the predictions were perfectly supported, then the data would lie
along the dashed brown lines in figures 5, A1. Prediction
(1) suggests that, after accounting for variation due to body
size, species in the same taxonomic/lifestyle group that
produce more offspring per litter might be expected to
produce offspring of smaller body size. This prediction is
supported in most groups (plots in right-hand columns
of figs. 5, A1; table 1) and is observed most clearly in the
lagomorphs (fig. 5D). Note that, in groups in which there
is usually only one offspring per litter, only limited variation is possible. This accounts for the unusual distributions observed in the plots for cetaceans, pinnipeds, and,
to a lesser extent, artiodactyls, bats, and primates (figs. 5,
A1). Caviomorph rodents and sea otters (Enhydra lutris)
produce litters of relatively few, large, precocial neonates,
as predicted (fig. A1), but there is only limited support
from hares (genus Lepus; fig. 5D).
7. A trade-off between allocation per litter and number
of litters per reproductive season will be evidenced as a
negative correlation among the normalization constants
of the various taxonomic/lifestyle groups. This prediction
is not supported overall (r9 p ⫺0.05, not significant; fig.
4A). Any evidence for the trade-off is obscured by the
variation in productivity, p, among the lifestyle groups,
which results in variation perpendicular to the q contours.
Table 1: Correlation coefficients r and associated P values for
the correlations between the residuals of allocation per litter
(z) and number of litters per reproductive season (y) and of
size of offspring (x) and their number (n)
Order
Artiodactyla
Cetacea
Chiroptera
Fissipeds
Insectivora
Lagomorpha
Pinnipeds
Primates
Rodentia
No. species
rzy
P
rxn
P
75
18
105
71
28
19
25
81
190
⫺.253
.070
.172
.383
⫺.089
⫺.411
⫺.221
⫺.191
.238
.029
.783
.079
.001
.654
.080
.288
.088
.001
⫺.572
⫺.553
⫺.299
⫺.302
⫺.238
⫺.682
.195
⫺.289
⫺.656
.000
.017
.002
.011
.223
.001
.349
.009
.000
Note: Data are from figures 5 and A1.
However, when variation in productivity is corrected for
using the standardization procedure of figure 3, there were
differences between the precocial, the carried, and the altricial groups (one-way ANOVA: F2, 8 p 7.1, P p .02). The
precocial mammals are farther to the right along a common q contour than the altricial group (Tukey’s multiple
comparison test: P ! .05). Using genus and family means
gave similar results (P ! .05 for genus, P ! .07 for family;
data in fig. A2), and the results are robust to errors in the
allometric regression coefficients (data in fig. A3). Mammals that carry their offspring are intermediate between
the precocial and the altricial mammals but are not significantly different from either. If this same trade-off holds
within lifestyle groups, species that produce more litters
per year should allocate less biomass to a litter. There is
little support for this prediction in most groups (plots in
left-hand columns of figs. 5, A1; table 1), with any tradeoff being obscured by wide variations in productivity
among species.
Discussion
We begin by emphasizing that we regard our predictions
as plausible testable hypotheses and that the above data
and analyses are only preliminary support for the predictions. We accept that additional analyses using improved
techniques and more and better data would be desirable.
For instance, for pragmatic reasons, we adopted parallellines models to identify differences between lifestyle groups
in figure 2, even though in some cases nonparallel-lines
models increase the proportion of variance explained. Our
method allows unambiguous quantitative comparisons of
trait values among groups across the entire range of body
sizes. Alternative methods that allow slopes to vary give
differences in trait value among groups that vary with body
size. Additional theoretical and empirical work is required
to assess the extent to which the framework that we have
Mammal Reproductive Strategies E193
presented provides additional insights into the observed
variation in mammalian life histories.
There is a long, rich literature on life-history theory
(e.g., MacArthur 1962; Charlesworth 1980; Charnov
1982). There is also a rich literature of accumulating data
on components of the life histories of diverse organisms,
including mammals (e.g., Gaillard et al. 1989; Promislow
and Harvey 1990; Purvis and Harvey 1995; Jones and
MacLarnon 2001; Charnov and Ernest 2006; Bielby et al.
2007). Much of this literature is phenomenological. It provides adaptive interpretations of patterns of variation in
terms of trade-offs, but it does not provide a conceptual
framework based on specified evolutionary mechanisms
and constraints. By contrast, our theory provides an explicitly mechanistic account of the evolution of mammal
life histories. These life histories are powerfully constrained
by the ability of females to acquire resources and convert
them into reproductive biomass. The rate of production
depends first on body size and second on lifestyle, as shown
in figure 2A in Sibly and Brown (2007; see also Brown
and Sibly 2006). Mass-specific productivity decreases as
body size increases because of unavoidable increases in the
costs of transporting resources around larger bodies. Productivity also depends on lifestyle, however, and this has
two important components: diet and mortality. When
body size is allowed for, mammals with more reliable and
abundant foods have higher rates of production, whereas
mammals with reduced mortality rates have lower productivity (Brown and Sibly 2006; Sibly and Brown 2007).
Our analyses focus on the allocation of productivity to
offspring between and within litters. The factor of primary
importance is how preweaning mortality varies with offspring size (fig. 1). Adaptive responses to mortality-size
relationships have resulted in the frequently observed precocial and altricial strategies, which segregate at opposite
ends of the trade-off between number and size of young
in a litter (fig. 4B). At one extreme, survival of offspring
born unprotected by a nest or burrow depends critically
on their abilities to escape predation and to thermoregulate, which in turn depend on size and developmental
state at birth, as in figure 1B. In these mammals, offspring
number is traded for size, so that females produce a few
large, precocial offspring, and offspring size is further increased by reducing litter frequency to increase litter mass.
Thus, selection increases offspring size in both trade-offs
so that some species produce only a single large offspring,
once per year. At the other extreme, juvenile survival is
relatively secure because offspring are protected in burrows
or nests, so the strategy is to produce many small, altricial
offspring. This is adaptive because, other things being
equal, more is better (i.e., results in higher fitness; fig. 1C),
and other things are more or less equal because survival
before weaning is not greatly affected by offspring size.
Litters are frequent, and, concomitantly, litter mass is
small, thereby minimizing the number of offspring that
die if the mother abandons them or dies before weaning.
A third distinct strategy is exhibited by mammals that carry
their young from birth until weaning. Their offspring are
not particularly large or precocial, but they do have adaptations to cling to the mother as she engages in all activities. There are few offspring per litter primarily because
of the difficulty of transporting and caring for more dependent offspring.
Mammals offer special challenges in developing and
testing life-history theory. For one thing, maternal investment in gestation and lactation makes it much more
difficult to perform the direct experimental manipulations
of number and size of offspring that are possible in other
groups such as birds and reptiles (e.g., Sinervo and Huey
1990; Fontaine and Martin 2006). Additionally, our results
suggest that, to account for the observed trade-offs in allocation of production, the single most important factor
is predation on juveniles and the way this varies with
neonate size. Unfortunately, few reliable data on the mortality-size relationship are available, due to the inherent
difficulties in measuring pre- and postweaning mortality
of free-living wild mammals (e.g., see Sibly et al. 1997).
Here we present a theoretical framework that overcomes
some of these limitations by using a new method to analyze
resource-allocation trade-offs. Our framework corrects for
variation in both body mass and rate of production (fig.
3) to reveal patterns of divergence along trade-off axes.
The usefulness of the method is particularly clear in figure
4A, where the divergence between altricial and precocial
mammals is not apparent until variation in productivity
is accounted for. This framework allows us to go beyond
earlier treatments in identifying the particular trade-offs
and lifestyles associated with the altricial, the precocial,
and the offspring-carrying strategies. The trade-off between offpring size and offspring number in figure 4B has
been shown previously (Read and Harvey 1989; Charnov
and Ernest 2006), as has the finding that precocial neonates
are heavier than altricial neonates (Martin 1984). When a
lifestyle group is constrained to produce altricial or precocial neonates, there are additional consequences and opportunities for selection and adaptation (Martin 1984;
Martin and McLarnon 1985; Harvey and Read 1988; Derrickson 1992).
Our analysis shows how ecological relationships have
led to the evolution of life-history trade-offs. When the
pervasive constraint of the allometry of production and
the effects of lifestyle have been accounted for, how preweaning mortality depends on offspring size is the primary
factor determining the trade-offs in allocation of resources
to reproduction. Further work is needed to assess similarities and differences among species within and among
E194 The American Naturalist
taxonomic and lifestyle groups (e.g., fig. 5) due to the
interplay between phylogenetic evolutionary relationships
and environmental conditions.
Acknowledgments
We thank K. E. Jones for supplying the bat data, E. L.
Charnov and members of the University of New Mexico/
Santa Fe Institute Scaling Group and the Integrating Mac-
roecological Pattern and Processes across Scales (IMPPS)/
National Science Foundation (NSF)–funded Research Coordination Network (RCN; DEB-0541625) for helpful discussions, and S. Beissinger and two reviewers for comments. This is IMPPS RCN publication 2 and was
supported by a Royal Society Travel Grant to R.M.S. and
an NSF grant (DEB-0083422) and a Packard Interdisciplinary Science Grant to J.H.B.
APPENDIX
Normalization Constants and Allometric Regression Coefficients of Production Rates and Life-History Characters
Table A1: Normalization constants of production rates and life-history characters (ⳲSEs)
No.
species
Order
Artiodactyla
Cetacea
Chiroptera
Fissipeds
Insectivora
Lagomorpha
Perissodactyla
Pinnipeds
Primates
Rodentia
Xenarthra
F10, 616
Adjusted R2
75
18
105
71
28
19
9
25
81
190
7
Production rate
per adult mass, qi
.614 Ⳳ
.701 Ⳳ
⫺.067 Ⳳ
.106 Ⳳ
.172 Ⳳ
.716 Ⳳ
.422 Ⳳ
.755 Ⳳ
.008 Ⳳ
.339 Ⳳ
.197 Ⳳ
36.6
73%
.040
.076
.052
.035
.061
.063
.094
.059
.034
.038
.099
Litters per
year, yi
Ⳳ .026
Ⳳ .049
Ⳳ .033
Ⳳ .023
Ⳳ .039
Ⳳ .040
Ⳳ .061
Ⳳ .038
Ⳳ .022
Ⳳ .025
Ⳳ .063
38.4
56%
.526
.234
.235
.421
.375
.794
.288
.496
.264
.543
.382
Litter mass per
adult mass, zi
Offspring per
litter, ni
.088 Ⳳ
.467 Ⳳ
⫺.303 Ⳳ
⫺.315 Ⳳ
⫺.203 Ⳳ
⫺.078 Ⳳ
.134 Ⳳ
.259 Ⳳ
⫺.256 Ⳳ
⫺.205 Ⳳ
⫺.185 Ⳳ
29.1
69%
.400 Ⳳ .021
.425 Ⳳ .040
.142 Ⳳ .028
.734 Ⳳ .019
.756 Ⳳ .033
.763 Ⳳ .033
.389 Ⳳ .050
.346 Ⳳ .032
.289 Ⳳ .018
.721 Ⳳ .020
.389 Ⳳ .053
152.8
75%
.028
.053
.036
.025
.043
.044
.066
.041
.024
.027
.069
Newborn mass
per adult mass, xi
⫺.312 Ⳳ
.042 Ⳳ
⫺.445 Ⳳ
⫺1.048 Ⳳ
⫺.959 Ⳳ
⫺.842 Ⳳ
⫺.255 Ⳳ
⫺.087 Ⳳ
⫺.545 Ⳳ
⫺.925 Ⳳ
⫺.573 Ⳳ
104.9
68%
.031
.058
.040
.027
.047
.048
.072
.045
.026
.029
.075
Note: Parameters qi, yi, zi, ni, and xi are as in equations (6). Normalization constants measure the vertical displacement of the regression
lines, that is, their y-intercepts at 1 g in figure 2 (see fig. 3; eq. [2]). The penultimate row gives F statistics from ANOVAs comparing the
normalization constants. The critical value at the 0.001% significance level is 4.2.
Table A2: Fitted regression coefficients with their SEs
Parameter
Regression coefficient
SE
⫺.3664
⫺.1076
⫺.2587
⫺.0673
⫺.1914
.017
.011
.012
.009
.013
bq
by
bz
bn
bx
Note: Parameters are as in equations (5).
Table A3: Statistics for a comparison of parallel-lines and nonparallel-lines models
Parameter
Production rate per adult mass, qi
Litters per year, yi
Litter mass per adult mass, zi
Offspring per litter, ni
Newborn mass per adult mass, xi
Note: NS p not significant.
F10, 606
P (parallel-lines model)
Adjusted R2 (%)
5.3
6.6
2.8
1.2
1.8
.000
.000
.002
NS
NS
75
59
70
75
69
E195
Figure A1: Scatter diagrams like those in figure 5 for the taxonomic/lifestyle groups not shown in that figure. One point did not fit in the lefthand column, a bear (Fissipeds, Ursidae) with coordinates (⫺1.20, ⫺0.03). Dashed brown lines connect strategies with the same value of the resource
¯ p 0 ; here (z ⫺ ¯z) represents the residual of z and (y ⫺
being allocated. Thus, the equation of the line in the left-hand panels is (z ⫺ ¯z) ⫹ (y ⫺ y)
ȳ) the residual of y. The line goes through the point (0, 0) because the mean of the residuals of each trait is 0. Similarly, the line in the right-hand
¯ ⫹ (n ⫺ n)
¯ p 0 . The caviomorphs are arrowed within the rodents and the sea otter within the fissipeds (see main
panels has the equation (x ⫺ x)
text).
E196
Figure A2: Scatterplots as in figure 4 (top) together with repeats of the analyses using genus means (middle) and family means (bottom).
E197
E198 The American Naturalist
Figure A3: Scatterplots as in figure 4, with allometric regression coefficients varied by Ⳳ2 SE.
Literature Cited
Bielby, J., G. M. Mace, O. R. P. Bininda-Emonds, M. Cardillo, J. L.
Gittleman, K. E. Jones, C. D. L. Orme, and A. Purvis. 2007. The
fast-slow continuum in mammalian life history: an empirical reevaluation. American Naturalist 169:748–757.
Brown, J. H., and R. M. Sibly. 2006. Life-history evolution under a
production constraint. Proceedings of the National Academy of
Sciences of the USA 103:17595–17599.
Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and G. B. West.
2004. Toward a metabolic theory of ecology. Ecology 85:1771–
1789.
Charlesworth, B. 1980. Evolution in age-structured populations.
Cambridge University Press, Cambridge.
Charnov, E. L. 1982. The theory of sex allocation. Princeton University Press, Princeton, NJ.
———. 1991. Evolution of life-history variation among female mammals. Proceedings of the National Academy of Sciences of the USA
88:1134–1137.
———. 1993. Life history invariants. Oxford University Press,
Oxford.
———. 2001. Evolution of mammal life histories. Evolutionary Ecology Research 3:521–535.
Charnov, E. L., and S. K. M. Ernest. 2006. The offspring-size/clutchsize trade-off in mammals. American Naturalist 167:578–582.
Charnov, E. L., R. Warne, and M. Moses. 2007. Lifetime reproductive
effort. American Naturalist 170:E129–E142.
Cody, M. L. 1966. A general theory of clutch size. Ecology 20:174–
184.
Derrickson, E. M. 1992. Comparative reproductive strategies of altricial and precocial eutherian mammals. Functional Ecology 6:
57–65.
Dobson, F. S. 2007. A lifestyle view of life-history evolution. Proceedings of the National Academy of Sciences of the USA 104:
17565–17566.
Ernest, S. K. M. 2003. Life history characteristics of placental nonvolant mammals. Ecology 84:3402.
Fontaine, J. J., and T. E. Martin. 2006. Parent birds assess nest pre-
dation risk and adjust their reproductive strategies. Ecology Letters
9:428–434.
Gaillard, J.-M., D. Pontier, D. Allainé, J.-D. Lebreton, J. Trouvilliez,
and J. Clobert. 1989. An analysis of demographic tactics in birds
and mammals. Oikos 56:59–76.
Harvey, P. H., and A. F. Read. 1988. How and why do mammalian
life histories vary? Pages 213–232 in M. S. Boyce, ed. Evolution
of life histories of mammals. Yale University Press, New Haven,
CT.
Jones, K. E., and A. MacLarnon. 2001. Bat life histories: testing models of mammalian life-history evolution. Evolutionary Ecology Research 3:465–476.
Kozlowski, J., and J. Weiner. 1997. Interspecific allometries are byproducts of body size optimization. American Naturalist 149:352–
380.
MacArthur, R. H. 1962. Some generalized theorems of natural selection. Proceedings of the National Academy of Sciences of the
USA 48:1893–1897.
Martin, R. D. 1984. Scaling effects and adaptive strategies in mammalian lactation. Symposia of the Zoological Society of London
51:81–117.
Martin, R. D., and A. M. McLarnon. 1985. Gestation period, neonatal
size and maternal investment in placental mammals. Nature 313:
220–223.
Oli, M. K. 2004. The fast-slow continuum and mammalian lifehistory patterns: an empirical evaluation. Basic and Applied Ecology 5:449–463.
Promislow, D. E. L., and P. H. Harvey. 1990. Living fast and dying
young: a comparative-analysis of life-history variation among
mammals. Journal of Zoology 220:417–437.
Purvis, A., and P. H. Harvey. 1995. Mammal life-history evolution:
a comparative test of Charnov’s model. Journal of Zoology 237:
259–283.
Read, A. F., and P. H. Harvey. 1989. Life-history differences among
the Eutherian radiations. Journal of Zoology 219:329–353.
Sibly, R. M., and J. H. Brown. 2007. Effects of body size and lifestyle
on evolution of mammal life histories. Proceedings of the National
Academy of Sciences of the USA 104:17707–17712.
Mammal Reproductive Strategies E199
Sibly, R. M., and P. Calow. 1986. Physiological ecology of animals.
Blackwell Scientific, Oxford.
———. 1987. Ecological compensation: a complication for testing
life-history theory. Journal of Theoretical Biology 125:177–186.
Sibly, R. M., and R. N. Curnow. 1993. An allelocentric view of lifehistory evolution. Journal of Theoretical Biology 160:533–546.
Sibly, R. M., D. Collett, D. E. L. Promislow, D. J. Peacock, and P.
H. Harvey. 1997. Mortality rates of mammals. Journal of Zoology
(London) 243:1–12.
Sinervo, B., and R. B. Huey. 1990. Allometric engineering: an experimental test of the causes of interpopulational differences in
performance. Science 248:1106–1109.
Sutherland, W. J., A. Grafen, and P. H. Harvey. 1986. Life history
correlations and demography. Nature 320:88.
Associate Editor: Tim Coulson
Editor: Donald L. DeAngelis